Hash functions are one of the most important cryptographic primitives. They
map an input of arbitrary finite length to a value of fixed length by compressing
the input, that is why, they are called hash. They must run ...

We have identified a completely integrable family of Monge-Ampère equations
through an examination of their Hamiltonian structure. Starting with a
variational formulation of the Monge-Ampère equations we have constructed
the ...

In this work by using the method of local interpolat ions suggested in [9] we
construct topological bases in the spaces of CP-functions defined on uniformly
perfect compact sets of Cantor type. Elements of the basis are ...

We consider a finite group acting as linear substitutions on a polynomial ring
and study the corresponding ring of invariants. Computing the invariant ring
and finding its ring theoretical properties is a classical ...

In this thesis, we consider some models of percolation in two dimensional
spaces. We study some numerical equalities and inequalities for the critical
probability, together with a general method for establishing strict ...

We consider all possible isomorphisms of cartesian products of Dragilev
spaces, and thanks to relations between the Dragilev functions of each factor
try to show that if there exists such an isomorphism, then any factor ...

In number theory theory, the class number of a field is a significant invariant.
All over the time, people have come up with formulas for some cases and in this
thesis I will discuss a proof of a class number formula for ...

In this thesis, we study the topology of the poset obtained by removing the
greatest and least elements of lattice of periods of a group action. For a G-set
X where G is a finite group, the lattice of periods is defined ...

We discuss the notion of Radon-Nikodym derivatives for operator valued completely
positive maps on C*-algebras, first introduced by Arveson [1969], and the
notion of absolute continuity for completely positive maps, ...

We give the definitions of finite volume Gibbs measure and limit Gibbs states.
In one dimensional Ising model with arbitrary boundary conditions we calculate
correlation functions in explicit way. In one dimension, ...

We consider some models of classical statistical mechanics with their random
perturbations and investigate the phase diagrams of this models. By using
uniqueness theorem we prove the absence of phase transitions in this models.

The purpose of this thesis is to obtain the estimate for the average mean
value of the remainder term of the asymptotic formula for the quadratic
mean value of the Fourier coefficients of the eigenfunctions over the ...

In this work we consider the spaces of Whitney functions defined on convergent
sequences of points.By means of linear topological invariants we analyze
linear topological structure of these spaces .Using diametral dimension ...

In generalization of [3] we will give the formula for the logarithmic dimension of
any Cantor-type set. We will demonstrate some applications of the logarithmic
dimension in Potential Theory. We will construct a polynomial ...

In this thesis, we study Lζ -modules, and using some exact sequences involving
Lζ -modules, we give an alternative proof to a theorem by Jon Carlson which says
that any ZG-module is a direct summand of a module which has ...

Constructing the Mackey group category M using axioms which are reminiscent
of fusion systems, the simple RM-functors (the simple functors from the R-linear
extension of M to R-modules, where R is a commutative ring) can ...

The Turkish Army like other organizations tries to keep up with the change
in all areas and uses some methods of change. One of the areas is management and
the method of change used by The Army is training and development ...

In this thesis we studied the notion of direct integral Hilbert spaces, first introduced
by J. von Neumann, and the closely related notion of decomposable
operators, as defined in Kadison and Ringrose [1997] and Abrahamse ...

Lorentzian Geometry has shown to be very useful in a wide range of studies
including many diverse research elds, especially in the theory of general relativity
and mathematical cosmology. A Walker manifold descends from ...

We introduce canonical induction formulae for some character rings of a finite
group, some of which follows from the formula for the complex character ring
constructed by Boltje. The rings we will investigate are the ...